334,289 research outputs found
The size of the pion from full lattice QCD with physical u, d, s and c quarks
We present the first calculation of the electromagnetic form factor of the π meson at physical light
quark masses. We use configurations generated by the MILC collaboration including the effect of u, d, s and c sea quarks with the Highly Improved Staggered Quark formalism. We work at three values of the lattice spacing on large volumes and with u/d quark masses going down to the physical value. We study scalar and vector form factors for a range in space-like q2 from 0.0 to -0.13 GeV2 and from their shape we extract mean square radii. Our vector form factor agrees well with experiment and we find hr2iV = 0:403(18)(6) fm2. For the scalar form factor we include quark-line disconnected
contributions which have a significant impact on the radius. We give the first results for SU(3) flavour-singlet and octet scalar mean square radii, obtaining: hr2isinglet
S = 0:506(38)(53)fm2 and hr2ioctet S = 0:431(38)(46)fm2. We discuss the comparison with expectations from chiral perturbation theory
Berezinskii-Kosterlitz-Thouless-like percolation transitions in the two-dimensional XY model
We study a percolation problem on a substrate formed by two-dimensional XY
spin configurations, using Monte Carlo methods. For a given spin configuration
we construct percolation clusters by randomly choosing a direction in the
spin vector space, and then placing a percolation bond between nearest-neighbor
sites and with probability ,
where governs the percolation process. A line of percolation thresholds
is found in the low-temperature range , where
is the XY coupling strength. Analysis of the correlation function , defined as the probability that two sites separated by a distance
belong to the same percolation cluster, yields algebraic decay for , and the associated critical exponent depends on and .
Along the threshold line , the scaling dimension for is,
within numerical uncertainties, equal to . On this basis, we conjecture
that the percolation transition along the line is of the
Berezinskii-Kosterlitz-Thouless type.Comment: 23 pages, 14 figure
Integrability of the symmetry reduced bosonic dynamics and soliton generating transformations in the low energy heterotic string effective theory
Integrable structure of the symmetry reduced dynamics of massless bosonic
sector of the heterotic string effective action is presented. For string
background equations that govern in the space-time of dimensions ()
the dynamics of interacting gravitational, dilaton, antisymmetric tensor and
any number of Abelian vector gauge fields, all depending only on two
coordinates, we construct an \emph{equivalent} matrix
spectral problem (). This spectral problem provides the base for the
development of various solution constructing procedures (dressing
transformations, integral equation methods). For the case of the absence of
Abelian gauge fields, we present the soliton generating transformations of any
background with interacting gravitational, dilaton and the second rank
antisymmetric tensor fields. This new soliton generating procedure is available
for constructing of various types of field configurations including stationary
axisymmetric fields, interacting plane, cylindrical or some other types of
waves and cosmological solutions.Comment: 4 pages; added new section on Belinski-Zakharov solitons and new
expressions for calculation of the conformal factor; corrected typo
Note on Redshift Distortion in Fourier Space
We explore features of redshift distortion in Fourier analysis of N-body
simulations. The phases of the Fourier modes of the dark matter density
fluctuation are generally shifted by the peculiar motion along the line of
sight, the induced phase shift is stochastic and has probability distribution
function (PDF) symmetric to the peak at zero shift while the exact shape
depends on the wave vector, except on very large scales where phases are
invariant by linear perturbation theory. Analysis of the phase shifts motivates
our phenomenological models for the bispectrum in redshift space. Comparison
with simulations shows that our toy models are very successful in modeling
bispectrum of equilateral and isosceles triangles at large scales. In the
second part we compare the monopole of the power spectrum and bispectrum in the
radial and plane-parallel distortion to test the plane-parallel approximation.
We confirm the results of Scoccimarro (2000) that difference of power spectrum
is at the level of 10%, in the reduced bispectrum such difference is as small
as a few percents. However, on the plane perpendicular to the line of sight of
k_z=0, the difference in power spectrum between the radial and plane-parallel
approximation can be more than 10%, and even worse on very small scales. Such
difference is prominent for bispectrum, especially for those configurations of
tilted triangles. The non-Gaussian signals under radial distortion on small
scales are systematically biased downside than that in plane-parallel
approximation, while amplitudes of differences depend on the opening angle of
the sample to the observer. The observation gives warning to the practice of
using the power spectrum and bispectrum measured on the k_z=0 plane as
estimation of the real space statistics.Comment: 15 pages, 8 figures. Accepted for publication in ChJA
Monodromy transform and the integral equation method for solving the string gravity and supergravity equations in four and higher dimensions
The monodromy transform and corresponding integral equation method described
here give rise to a general systematic approach for solving integrable
reductions of field equations for gravity coupled bosonic dynamics in string
gravity and supergravity in four and higher dimensions. For different types of
fields in space-times of dimensions with commuting isometries
-- stationary fields with spatial symmetries, interacting waves or partially
inhomogeneous cosmological models, the string gravity equations govern the
dynamics of interacting gravitational, dilaton, antisymmetric tensor and any
number of Abelian vector gauge fields (all depending only on two
coordinates). The equivalent spectral problem constructed earlier allows to
parameterize the infinite-dimensional space of local solutions of these
equations by two pairs of \cal{arbitrary} coordinate-independent holomorphic
- and - matrix functions of a spectral parameter which constitute a complete set
of monodromy data for normalized fundamental solution of this spectral problem.
The "direct" and "inverse" problems of such monodromy transform --- calculating
the monodromy data for any local solution and constructing the field
configurations for any chosen monodromy data always admit unique solutions. We
construct the linear singular integral equations which solve the inverse
problem. For any \emph{rational} and \emph{analytically matched} (i.e.
and
) monodromy data the solution for string
gravity equations can be found explicitly. Simple reductions of the space of
monodromy data leads to the similar constructions for solving of other
integrable symmetry reduced gravity models, e.g. 5D minimal supergravity or
vacuum gravity in dimensions.Comment: RevTex 7 pages, 1 figur
Motivic invariants of Artin stacks and 'stack functions'
An invariant I of quasiprojective K-varieties X with values in a commutative
ring R is "motivic" if I(X)= I(Y)+I(X\Y) for Y closed in X, and I(X x
Y)=I(X)I(Y). Examples include Euler characteristics chi and virtual Poincare
and Hodge polynomials.
We first define a unique extension I' of I to finite type Artin K-stacks F,
which is motivic and satisfies I'([X/G])=I(X)/I(G) when X is a K-variety, G a
"special" K-group acting on X, and [X/G] is the quotient stack. This only works
if I(G) is invertible in R for all special K-groups G, which excludes I=chi as
chi(K*)=0. But we can extend the construction to get round this.
Then we develop the theory of "stack functions" on Artin stacks. These are a
universal generalization of constructible functions on Artin stacks, as studied
in the author's paper math.AG/0403305. There are several versions of the
construction: the basic one SF(F), and variants SF(F,I,R),... "twisted" by
motivic invariants. We associate a Q-vector space SF(F) or an R-module
SF(F,I,R) to each Artin stack F, with functorial operations of multiplication,
pullbacks phi^* and pushforwards phi_* under 1-morphisms phi : F --> G, and so
on. They will be important tools in the author's series on "Configurations in
abelian categories", math.AG/0312190, math.AG/0503029, math.AG/0410267 and
math.AG/0410268.Comment: 48 pages. (v4) Final version, to appear in Quarterly Journal of
Mathematic
Magneto-optical Kerr effect in Weyl semimetals with broken inversion and time-reversal symmetries
The topological nature of the band structure of a Weyl semimetal leads to a
number of unique transport and optical properties. For example, the description
of the propagation of an electromagnetic wave in a Weyl semimetal with broken
time-reversal and inversion symmetry, for example, requires a modification of
the Maxwell equations by the axion field where is the separation
in wave vector space between two Weyl nodes of opposite chiralities and
is their separation in energy. In this paper, we study
theoretically how the axion terms and modify the frequency
behavior of the Kerr rotation and ellipticity angles and in a Weyl semimetal. Both the
Faraday and Voigt configurations are considered since they provide different
information on the electronic transitions and plasmon excitation. We derive the
Kerr angles firstly without an external magnetic field where the rotation of
the polarization is only due to the axion terms and secondly in a strong
magnetic field where these terms compete with the gyration effect of the
magnetic field. In this latter case, we concentrate on the ultra-quantum limit
where the Fermi level lies in the chiral Landau level and the Kerr and
ellipticity angles have more complex frequency and magnetic field behaviors.Comment: 21 pages with 14 PDF figure
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